math.tan

Three distinct suites: educational examples on the calculator page, this legacy regression count (25/25 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

This calculator CURRENT · Public schema 1.0.4 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-09-08.policy. Calculation version 1.0.4. CVP 1.0.0-proposed. 4/4 golden · 10/10 CVP boundary · 8/8 invalid · 5/5 property · 4/4 metamorphic · 4/4 round-trip · 16/16 O3 · 1/1 cross-interface · 11/11 cross-calculator · 4/4 URL→result→graph · 1/1 CVP contract. digest 494caf2c4f61. ≤2 ULP vs O3 applies to the 16 published tabulated vectors (common angles away from poles plus 8 seeded random angles in (−50°, 50°)). It is not a guarantee over the entire real line, including poles, huge angles, or unlisted neighborhoods of zeros.

• Golden (oracle-backed) 4 / 4
• CVP boundary 10 / 10
• Invalid input 8 / 8
• Property 5 / 5
• Metamorphic 4 / 4
• Round-trip 4 / 4
• O3 high-precision 16 / 16
• Cross-interface 1 / 1
• Cross-calculator 11 / 11
• URL → result → graph 4 / 4
• CVP contract 1 / 1
• Interfaces PASS · UI (SSR) / REST / MCP / URL→result→graph
• Interface claim Success 1/1. Integration: URL → SSR result → Live graph current point (4/4). Hydration/slider/history are URL-canonical contracts, not a live browser session.
• Assurance Core

• release artifacts aligned PASS
• schema valid input executes PASS
• engine success output validates schema PASS

Fingerprint sha256:672b0a252bc3ec1ae680516503c13aaddd3a8e304d3c94d640505752aa2b42cd

Input schema sha256:a145c86bf4295643a515b07cddf823049424a88c3a7fc25e463dfc92773671b6 · Output schema sha256:c6e4f75fa48f8b655778eb2014eee65632aa82db1d919d28c89fbd08e417449c · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Tool

tan

Engine

tan

Engine build

2026-09-10

Evidence core

2026-09-10T22:48:17.762Z

Rendered

2026-09-16T22:03:43.779Z

Last reviewed

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Assumptions

• Real tangent only. Inverse is Arctan, not this published engine.
• Documented pole classification: UNDEFINED when distance to 90° + 180°k is < 1e-12°. That threshold is a numerical classification policy, not a claim that those inputs are mathematically exact odd multiples of 90°. |cos(θ)| is not used as a pole test.
• If the input is not classified as a pole and distance-to-pole < 0.01°, the engine returns a finite tan(θ) with warnings: [{ code: NEAR_SINGULARITY }]. status remains ok.
• Documented common-angle snap: after reducing mod 360°, an input within 1e-12° of a listed common angle (0, ±30, ±45, ±60, …) is replaced by the algebraic value (0, ±1/√3, ±1, ±√3). This is a snap policy, not mathematical exactness. Nearby inputs such as 60.00000005° keep IEEE-754 Math.tan.
• Documented cleanup: if no snap applies and |y| < 1e-12, the engine rewrites y to 0. That changes the IEEE-754 result for some non-zero inputs; it is a cleanup policy, not a mathematical identity.

Limitations

• Exact poles (90° + 180°k) → UNDEFINED
• Within 0.01° of a pole → finite value with warnings NEAR_SINGULARITY
• Missing theta → MISSING_REQUIRED_INPUT